What is 4/(x-3)<= 2/(x-2) ?

The solution to 4/(x-3)<= 2/(x-2) is x<= 1\lor 2<x<3

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4/(x-3)<= 2/(x-2)

\frac{4}{x - 3} \leq \frac{2}{x - 2}

x \leq 1 or 2 < x < 3

Interval Notation

(- \infty, 1] \cup (2, 3)

Solution steps

\frac{4}{x - 3} \leq \frac{2}{x - 2}

Rewrite in standard form

\frac{2 x - 2}{( x - 3 ) ( x - 2 )} \leq 0

Factor

\frac{2 x - 2}{( x - 3 ) ( x - 2 )} : \frac{2 ( x - 1 )}{( x - 3 ) ( x - 2 )}

\frac{2 ( x - 1 )}{( x - 3 ) ( x - 2 )} \leq 0

Divide both sides by

2

\frac{\frac{2 ( x - 1 )}{( x - 3 ) ( x - 2 )}}{2} \leq \frac{0}{2}

Simplify

\frac{x - 1}{( x - 3 ) ( x - 2 )} \leq 0

Identify the intervals

x \leq 1 or 2 < x < 3

n^{2} + 11 n + 30 = 0

3 x^{2} + 9 x - 2 x - 6 = 0

\frac{2 π}{\frac{4 π}{3}}

(- 128)^{\frac{1}{7}}

288 x^{2} y^{5}

What is 4/(x-3)<= 2/(x-2) ?
The solution to 4/(x-3)<= 2/(x-2) is x<= 1\lor 2<x<3